A circular field of radius has a chord that subtends an angle of at the centre
MATHEMATICS · Multi-part · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles
Problem
A circular field of radius 28m has a chord that subtends an angle of 120∘ at the centre. The soil in the region between the chord and the corresponding arc is to be excavated to a uniform depth of 0.5m to form a pond. Take π=722.
(i) Calculate the area of the sector formed by the radii and the intercepted arc.
(ii) Determine the area of the triangle enclosed by the radii and the chord.
(iii) Hence find the area of the segment that will become the pond.
(iv) Calculate the volume of earth (in m3) that must be removed to the given depth.